Got kids (or adults) who won’t eat eggplant/aubergine? I do, but they eat this because it’s fun, not to mention delicious. Just about every bite contains long, stringy stretches of gooey smoked cheese (the recipe name refers back to the days of telephones with long cords — remember those?). The best time to make this southern Italian–inspired dish is in mid to late summer, when eggplants/aubergines are in abundance at farmers’ markets and you can take your pick of the younger ones — firm, fleshy, and no bitter juices.
Bring a large pot of water to a rolling boil and salt generously. Lightly coat a 9-by-13-inch baking dish with vegetable oil and set aside.
Pour vegetable oil to a depth of ¼-inch into a large frying pan and heat over medium-high heat. Place a platter lined with a double layer of paper towels/absorbent paper or a large, plain brown-paper bag near the stove.
Add the eggplant/aubergine cubes to the hot oil in small batches to avoid crowding the pan, and fry, turning them a couple of times, for about 5 minutes total, or until golden brown on all sides. Use a slotted spoon to remove the eggplant cubes to the prepared platter. Repeat until all the cubes are fried.
Transfer the fried eggplant to a large bowl and spoon a little of the tomato sauce on top. Gently toss the cubes with the sauce until the cubes are evenly coated. Set aside.
Heat the oven to 375 degrees.
Add the pasta to the boiling water, stir to separate, and cook according to the manufacturer’s instructions until not quite al dente. They should be slightly underdone, as they will finish cooking in the oven. Drain the pasta in a colander set in the sink, reserving about 1 cup of the cooking water.
Transfer the pasta to a very large bowl and spoon about two-thirds of the sauce over it. Gently toss the pasta and sauce to combine thoroughly. Add the eggplant, smoked mozzarella, smoked scamorza, and basil to the bowl. Using a large wooden spoon or spatula, gently toss the pasta, eggplant, cheeses, and basil together. Taste and add salt, if you like.
Spoon the pasta mixture into the prepared baking dish and spoon some additional sauce on top. You may not need all of the remaining sauce. Use just enough to keep the pasta moist, so that it will absorb the liquid and finish cooking in the oven. Sprinkle the Parmigiano cheese on top. Cover the dish with aluminum foil.
Bake for 15 minutes. Uncover and bake for 15–20 minutes longer, or until the cheese is melted and bubbly and the top is nicely browned and crisp around the edges. Let stand for 5 minutes before serving.